4 "cell_type": "markdown",
7 "# Interleaved strings\n",
9 "Given two strings a and b and a target c, could c be formed form some interleaving/merge of a and b?\n",
16 "When s3 = \"aadbbcbcac\", return true.\n",
17 "When s3 = \"aadbbbaccc\", return false."
43 "s3t = \"aadbbcbcac\"\n",
44 "s3f = \"aadbbbaccc\""
55 "[(0, ''), (1, 'a'), (2, 'aa'), (3, 'aab'), (4, 'aabc'), (5, 'aabcc')]"
60 "output_type": "execute_result"
64 "[(i, s1[:i]) for i in range(len(s1)+1)]"
68 "cell_type": "markdown",
71 "`dp_table[i, j]` is True if first `i` + `j` characters of `s3` can be formed from interleaving of first `i` characters of `s1` and first `j` characters of `s2`."
82 "[[True, False, False, False, False, False],\n",
83 " [False, False, False, False, False, False],\n",
84 " [False, False, False, False, False, False],\n",
85 " [False, False, False, False, False, False],\n",
86 " [False, False, False, False, False, False],\n",
87 " [False, False, False, False, False, False]]"
92 "output_type": "execute_result"
96 "dp_table = [[False] * (len(s1) + 1) for _ in range(len(s2) + 1)]\n",
97 "dp_table[0][0] = True\n",
103 "execution_count": 5,
149 "execution_count": 5,
151 "output_type": "execute_result"
155 "dp_table = {(i, j): False\n",
156 " for i in range(len(s1)+1)\n",
157 " for j in range(len(s2)+1)}\n",
163 "execution_count": 6,
169 "def show_table(table):\n",
170 " return '\\n'.join(\n",
171 " ' '.join(str(table[i, j])[0] for j in sorted(set([k[1] for k in table])))\n",
172 " for i in sorted(set([k[0] for k in table]))) "
177 "execution_count": 7,
183 "def show_table(table):\n",
184 " return '\\n'.join(\n",
185 " ' '.join('T' if table[i, j] else '.' for j in sorted(set([k[1] for k in table])))\n",
186 " for i in sorted(set([k[0] for k in table]))) "
191 "execution_count": 8,
196 "output_type": "stream",
208 "print(show_table(dp_table))"
213 "execution_count": 9,
218 "output_type": "stream",
220 "aabcc dbbca aadbbcbcac\n",
221 "aa 0 0 ! ! ! True\n",
222 "s2 0 1 ! d a False\n",
223 "s2 0 2 ! b a False\n",
224 "s2 0 3 ! b d False\n",
225 "s2 0 4 ! c b False\n",
226 "s2 0 5 ! a b False\n",
227 "s1 1 0 a ! a True\n",
228 "xx 1 1 a d a False\n",
229 "xx 1 2 a b d False\n",
230 "xx 1 3 a b b False\n",
231 "xx 1 4 a c b False\n",
232 "xx 1 5 a a c False\n",
233 "s1 2 0 a ! a True\n",
234 "s2 2 1 a d d True\n",
235 "s2 2 2 a b b True\n",
236 "s2 2 3 a b b True\n",
237 "s2 2 4 a c c True\n",
238 "xx 2 5 a a b False\n",
239 "s1 3 0 b ! d False\n",
240 "s1 3 1 b d b True\n",
241 "s2 3 2 b b b True\n",
242 "s1 3 2 b b b True\n",
243 "xx 3 3 b b c False\n",
244 "s1 3 4 b c b True\n",
245 "xx 3 5 b a c False\n",
246 "s1 4 0 c ! b False\n",
247 "xx 4 1 c d b False\n",
248 "s1 4 2 c b c True\n",
249 "s2 4 3 c b b True\n",
250 "s2 4 4 c c c True\n",
251 "s1 4 4 c c c True\n",
252 "s2 4 5 c a a True\n",
253 "s1 5 0 c ! b False\n",
254 "xx 5 1 c d c False\n",
255 "xx 5 2 c b b False\n",
256 "s1 5 3 c b c True\n",
257 "xx 5 4 c c a False\n",
258 "s1 5 5 c a c True\n",
270 "{(1, 0): (0, 0, 'a', 's1'),\n",
271 " (2, 0): (1, 0, 'a', 's1'),\n",
272 " (2, 1): (2, 0, 'd', 's2'),\n",
273 " (2, 2): (2, 1, 'b', 's2'),\n",
274 " (2, 3): (2, 2, 'b', 's2'),\n",
275 " (2, 4): (2, 3, 'c', 's2'),\n",
276 " (3, 1): (2, 1, 'b', 's1'),\n",
277 " (3, 2): (2, 2, 'b', 's1'),\n",
278 " (3, 4): (2, 4, 'b', 's1'),\n",
279 " (4, 2): (3, 2, 'c', 's1'),\n",
280 " (4, 3): (4, 2, 'b', 's2'),\n",
281 " (4, 4): (3, 4, 'c', 's1'),\n",
282 " (4, 5): (4, 4, 'a', 's2'),\n",
283 " (5, 3): (4, 3, 'c', 's1'),\n",
284 " (5, 5): (4, 5, 'c', 's1')}"
287 "execution_count": 9,
289 "output_type": "execute_result"
295 "print(s1, s2, s3)\n",
297 "dp_table = {(i, j): False\n",
298 " for i in range(len(s1)+1)\n",
299 " for j in range(len(s2)+1)}\n",
301 "backpointers = {}\n",
303 "for i in range(len(s1)+1):\n",
304 " for j in range(len(s2)+1):\n",
305 " if i == 0 and j == 0:\n",
306 " dp_table[i, j] = True\n",
307 " print('aa', i, j, '!', '!', '!', dp_table[i, j])\n",
309 " # extend by character from s2\n",
310 " if dp_table[i, j-1] and s2[j-1] == s3[i+j-1]:\n",
311 " dp_table[i, j] = True\n",
312 " backpointers[i, j] = (i, j-1, s2[j-1], 's2')\n",
313 " print('s2', i, j, '!', s2[j-1], s3[i+j-1], dp_table[i, j])\n",
315 " # extend by character from s1\n",
316 " if dp_table[i-1, j] and s1[i-1] == s3[i+j-1]:\n",
317 " dp_table[i, j] = True\n",
318 " backpointers[i, j] = (i-1, j, s1[i-1], 's1')\n",
319 " print('s1', i, j, s1[i-1], '!', s3[i+j-1], dp_table[i, j])\n",
321 " # extend by character from s2\n",
322 " if dp_table[i, j-1] and s2[j-1] == s3[i+j-1]:\n",
323 " dp_table[i, j] = True\n",
324 " backpointers[i, j] = (i, j-1, s2[j-1], 's2')\n",
325 " print('s2', i, j, s1[i-1], s2[j-1], s3[i+j-1], dp_table[i, j]) \n",
326 " # extend by character from s1\n",
327 " if dp_table[i-1, j] and s1[i-1] == s3[i+j-1]:\n",
328 " dp_table[i, j] = True\n",
329 " backpointers[i, j] = (i-1, j, s1[i-1], 's1') \n",
330 " print('s1', i, j, s1[i-1], s2[j-1], s3[i+j-1], dp_table[i, j])\n",
331 " if not dp_table[i, j]:\n",
332 " print('xx', i, j, s1[i-1], s2[j-1], s3[i+j-1], dp_table[i, j])\n",
334 "print(show_table(dp_table))\n",
340 "execution_count": 10,
346 "def is_interleave(seq1, seq2, seq3, return_backpointers=False, return_table=False, debug=False):\n",
347 " \"\"\"Return true if seq3 is some interleaved merge of seq1 and seq2.\n",
348 " If return_backpointers, also return the set of backpointers to\n",
349 " reconstruct the interleaving\"\"\"\n",
351 " # dp_table[i, j] is True if first i+j characters of seq is made up of \n",
352 " # an interleaving of the first i characters of seq1 and the \n",
353 " # first j characters of seq2\n",
355 " if len(seq1) + len(seq2) != len(seq3):\n",
356 " if return_backpointers or return_table:\n",
357 " retval = [False]\n",
358 " if return_backpointers:\n",
360 " if return_table:\n",
362 " return tuple(retval)\n",
366 " dp_table = {(i, j): False\n",
367 " for i in range(len(seq1)+1)\n",
368 " for j in range(len(seq2)+1)}\n",
370 " backpointers = {}\n",
372 " for i in range(len(seq1)+1):\n",
373 " for j in range(len(seq2)+1):\n",
374 " if i == 0 and j == 0:\n",
375 " dp_table[i, j] = True\n",
376 " if debug: print('xxxx', i, j, '!', '!', '!', dp_table[i, j])\n",
378 " # extend by character from seq2\n",
379 " if dp_table[i, j-1] and seq2[j-1] == seq3[i+j-1]:\n",
380 " dp_table[i, j] = True\n",
381 " backpointers[i, j] = (i, j-1, seq2[j-1], 'seq2')\n",
382 " if debug: print('seq2', i, j, '!', seq2[j-1], seq3[i+j-1], dp_table[i, j])\n",
384 " # extend by character from seq1\n",
385 " if dp_table[i-1, j] and seq1[i-1] == seq3[i+j-1]:\n",
386 " dp_table[i, j] = True\n",
387 " backpointers[i, j] = (i-1, j, seq1[i-1], 'seq1')\n",
388 " if debug: print('seq1', i, j, seq1[i-1], '!', seq3[i+j-1], dp_table[i, j])\n",
390 " # extend by character from seq2\n",
391 " if dp_table[i, j-1] and seq2[j-1] == seq3[i+j-1]:\n",
392 " dp_table[i, j] = True\n",
393 " backpointers[i, j] = (i, j-1, seq2[j-1], 'seq2')\n",
394 " if debug: print('seq2', i, j, seq1[i-1], seq2[j-1], seq3[i+j-1], dp_table[i, j]) \n",
395 " # extend by character from seq1\n",
396 " if dp_table[i-1, j] and seq1[i-1] == seq3[i+j-1]:\n",
397 " dp_table[i, j] = True\n",
398 " backpointers[i, j] = (i-1, j, seq1[i-1], 'seq1') \n",
399 " if debug: print('seq1', i, j, seq1[i-1], seq2[j-1], seq3[i+j-1], dp_table[i, j])\n",
400 " if not dp_table[i, j]:\n",
401 " if debug: print('xxxx', i, j, seq1[i-1], seq2[j-1], seq3[i+j-1], dp_table[i, j])\n",
403 " if return_backpointers or return_table:\n",
404 " retval = [dp_table[len(seq1), len(seq2)]]\n",
405 " if return_backpointers:\n",
406 " retval += [backpointers]\n",
407 " if return_table:\n",
408 " retval += [dp_table]\n",
409 " return tuple(retval)\n",
411 " return dp_table[len(seq1), len(seq2)]"
416 "execution_count": 11,
425 "execution_count": 11,
427 "output_type": "execute_result"
431 "is_interleave(s1, s2, s3t)"
436 "execution_count": 12,
443 " {(1, 0): (0, 0, 'a', 'seq1'),\n",
444 " (2, 0): (1, 0, 'a', 'seq1'),\n",
445 " (2, 1): (2, 0, 'd', 'seq2'),\n",
446 " (2, 2): (2, 1, 'b', 'seq2'),\n",
447 " (2, 3): (2, 2, 'b', 'seq2'),\n",
448 " (2, 4): (2, 3, 'c', 'seq2'),\n",
449 " (3, 1): (2, 1, 'b', 'seq1'),\n",
450 " (3, 2): (2, 2, 'b', 'seq1'),\n",
451 " (3, 4): (2, 4, 'b', 'seq1'),\n",
452 " (4, 2): (3, 2, 'c', 'seq1'),\n",
453 " (4, 3): (4, 2, 'b', 'seq2'),\n",
454 " (4, 4): (3, 4, 'c', 'seq1'),\n",
455 " (4, 5): (4, 4, 'a', 'seq2'),\n",
456 " (5, 3): (4, 3, 'c', 'seq1'),\n",
457 " (5, 5): (4, 5, 'c', 'seq1')})"
460 "execution_count": 12,
462 "output_type": "execute_result"
466 "is_interleave(s1, s2, s3t, return_backpointers=True)"
471 "execution_count": 13,
480 " {(1, 0): (0, 0, 'a', 'seq1'),\n",
481 " (2, 0): (1, 0, 'a', 'seq1'),\n",
482 " (2, 1): (2, 0, 'd', 'seq2'),\n",
483 " (2, 2): (2, 1, 'b', 'seq2'),\n",
484 " (2, 3): (2, 2, 'b', 'seq2'),\n",
485 " (2, 4): (2, 3, 'c', 'seq2'),\n",
486 " (3, 1): (2, 1, 'b', 'seq1'),\n",
487 " (3, 2): (2, 2, 'b', 'seq1'),\n",
488 " (3, 4): (2, 4, 'b', 'seq1'),\n",
489 " (4, 2): (3, 2, 'c', 'seq1'),\n",
490 " (4, 3): (4, 2, 'b', 'seq2'),\n",
491 " (4, 4): (3, 4, 'c', 'seq1'),\n",
492 " (4, 5): (4, 4, 'a', 'seq2'),\n",
493 " (5, 3): (4, 3, 'c', 'seq1'),\n",
494 " (5, 5): (4, 5, 'c', 'seq1')},\n",
533 "execution_count": 13,
535 "output_type": "execute_result"
539 "is_interleave(s1, s2, s3t, return_backpointers=True, return_table=True)"
544 "execution_count": 14,
553 "execution_count": 14,
555 "output_type": "execute_result"
559 "is_interleave(s1, s2, s3f)"
564 "execution_count": 15,
569 "output_type": "stream",
571 "xxxx 0 0 ! ! ! True\n",
572 "seq2 0 1 ! b a False\n",
573 "seq2 0 2 ! b a False\n",
574 "seq2 0 3 ! b a False\n",
575 "seq1 1 0 a ! a True\n",
576 "xxxx 1 1 a b a False\n",
577 "xxxx 1 2 a b a False\n",
578 "xxxx 1 3 a b b False\n",
579 "seq1 2 0 a ! a True\n",
580 "xxxx 2 1 a b a False\n",
581 "xxxx 2 2 a b b False\n",
582 "xxxx 2 3 a b a False\n",
583 "seq1 3 0 a ! a True\n",
584 "seq2 3 1 a b b True\n",
585 "xxxx 3 2 a b a False\n",
586 "xxxx 3 3 a b b False\n",
587 "seq1 4 0 a ! b False\n",
588 "seq1 4 1 a b a True\n",
589 "seq2 4 2 a b b True\n",
590 "seq2 4 3 a b b True\n"
597 " {(1, 0): (0, 0, 'a', 'seq1'),\n",
598 " (2, 0): (1, 0, 'a', 'seq1'),\n",
599 " (3, 0): (2, 0, 'a', 'seq1'),\n",
600 " (3, 1): (3, 0, 'b', 'seq2'),\n",
601 " (4, 1): (3, 1, 'a', 'seq1'),\n",
602 " (4, 2): (4, 1, 'b', 'seq2'),\n",
603 " (4, 3): (4, 2, 'b', 'seq2')})"
606 "execution_count": 15,
608 "output_type": "execute_result"
612 "is_interleave('aaaa', 'bbb', 'aaababb', return_backpointers=True, debug=True)"
617 "execution_count": 16,
623 "def show_backtrace(bps):\n",
624 " i = max([0] + [k[0] for k in bps])\n",
625 " j = max([0] + [k[1] for k in bps])\n",
627 " if (i, j) in bps:\n",
628 " while i != 0 or j != 0:\n",
629 " if bps[i, j][3] == 'seq1':\n",
630 " chars += bps[i, j][2].upper()\n",
632 " chars += bps[i, j][2]\n",
633 " i, j = bps[i, j][0], bps[i, j][1] \n",
634 " return ''.join(list(reversed(chars)))\n",
641 "execution_count": 17,
647 "def make_string(length, alphabet=None):\n",
648 " if not alphabet:\n",
649 " alphabet = 'abcdefgh'\n",
650 " return ''.join(random.choice(alphabet) for _ in range(length)) "
655 "execution_count": 18,
661 "'cccbggadggfbghfbeeeecgabbcdehcgfdhegefddahcdcabbch'"
664 "execution_count": 18,
666 "output_type": "execute_result"
675 "execution_count": 19,
681 "def interleave(s1, s2, wander_limit=10, debug=False):\n",
682 " i1 = i2 = wander = 0\n",
683 " interleaved = []\n",
684 " while i1 <= len(s1) and i2 <= len(s2):\n",
685 " if i1 == len(s1):\n",
686 " if debug: print(i1, i2, wander, 'remaining s2', s2[i2:])\n",
687 " interleaved += s2[i2:]\n",
688 " i2 = len(s2) + 1\n",
689 " elif i2 == len(s2):\n",
690 " if debug: print(i1, i2, wander, 'remaining s1', s1[i1:])\n",
691 " interleaved += s1[i1:]\n",
692 " i1 = len(s1) + 1\n",
694 " if wander == wander_limit:\n",
696 " elif wander == -wander_limit:\n",
699 " step = random.choice([+1, -1])\n",
701 " if debug: print(i1, i2, wander, 'adding', s1[i1])\n",
702 " interleaved += s1[i1]\n",
706 " if debug: print(i1, i2, wander, 'adding', s2[i2])\n",
707 " interleaved += s2[i2]\n",
710 " return ''.join(interleaved)\n",
716 "execution_count": 20,
721 "output_type": "stream",
743 "10 10 0 adding v\n",
744 "10 11 -1 adding c\n",
745 "11 11 0 adding f\n",
746 "12 11 1 adding a\n",
747 "13 11 2 adding y\n",
748 "13 12 1 adding y\n",
749 "13 13 0 adding y\n",
750 "13 14 -1 adding u\n",
751 "13 15 -2 adding e\n",
752 "14 15 -1 adding z\n",
753 "14 16 -2 adding e\n",
754 "15 16 -1 adding b\n",
755 "16 16 0 adding c\n",
756 "17 16 1 adding g\n",
757 "18 16 2 adding w\n",
758 "18 17 1 adding u\n",
759 "18 18 0 adding e\n",
760 "19 18 1 adding w\n",
761 "19 19 0 adding b\n",
762 "20 19 1 remaining s2 y\n"
768 "('cafehbhfdccfaeebcgeb',\n",
769 " 'xvuzywuxzuvyyyuzwuwy',\n",
770 " 'xcvafuzyweuhxbhzfdcuvcfayyyuezebcgwuewby',\n",
774 "execution_count": 20,
776 "output_type": "execute_result"
780 "s1 = make_string(20)\n",
781 "s2 = make_string(20, alphabet='uvwxyz')\n",
782 "il = interleave(s1, s2, wander_limit=5, debug=True)\n",
783 "s1, s2, il, len(il)"
788 "execution_count": 21,
793 "output_type": "stream",
795 "xxxx 0 0 ! ! ! True\n",
796 "seq2 0 1 ! c x False\n",
797 "seq2 0 2 ! a c False\n",
798 "seq2 0 3 ! f v False\n",
799 "seq2 0 4 ! e a False\n",
800 "seq2 0 5 ! h f False\n",
801 "seq2 0 6 ! b u False\n",
802 "seq2 0 7 ! h z False\n",
803 "seq2 0 8 ! f y False\n",
804 "seq2 0 9 ! d w False\n",
805 "seq2 0 10 ! c e False\n",
806 "seq2 0 11 ! c u False\n",
807 "seq2 0 12 ! f h False\n",
808 "seq2 0 13 ! a x False\n",
809 "seq2 0 14 ! e b False\n",
810 "seq2 0 15 ! e h False\n",
811 "seq2 0 16 ! b z False\n",
812 "seq2 0 17 ! c f False\n",
813 "seq2 0 18 ! g d False\n",
814 "seq2 0 19 ! e c False\n",
815 "seq2 0 20 ! b u False\n",
816 "seq1 1 0 x ! x True\n",
817 "seq2 1 1 x c c True\n",
818 "xxxx 1 2 x a v False\n",
819 "xxxx 1 3 x f a False\n",
820 "xxxx 1 4 x e f False\n",
821 "xxxx 1 5 x h u False\n",
822 "xxxx 1 6 x b z False\n",
823 "xxxx 1 7 x h y False\n",
824 "xxxx 1 8 x f w False\n",
825 "xxxx 1 9 x d e False\n",
826 "xxxx 1 10 x c u False\n",
827 "xxxx 1 11 x c h False\n",
828 "xxxx 1 12 x f x False\n",
829 "xxxx 1 13 x a b False\n",
830 "xxxx 1 14 x e h False\n",
831 "xxxx 1 15 x e z False\n",
832 "xxxx 1 16 x b f False\n",
833 "xxxx 1 17 x c d False\n",
834 "xxxx 1 18 x g c False\n",
835 "xxxx 1 19 x e u False\n",
836 "xxxx 1 20 x b v False\n",
837 "seq1 2 0 v ! c False\n",
838 "seq1 2 1 v c v True\n",
839 "seq2 2 2 v a a True\n",
840 "seq2 2 3 v f f True\n",
841 "xxxx 2 4 v e u False\n",
842 "xxxx 2 5 v h z False\n",
843 "xxxx 2 6 v b y False\n",
844 "xxxx 2 7 v h w False\n",
845 "xxxx 2 8 v f e False\n",
846 "xxxx 2 9 v d u False\n",
847 "xxxx 2 10 v c h False\n",
848 "xxxx 2 11 v c x False\n",
849 "xxxx 2 12 v f b False\n",
850 "xxxx 2 13 v a h False\n",
851 "xxxx 2 14 v e z False\n",
852 "xxxx 2 15 v e f False\n",
853 "xxxx 2 16 v b d False\n",
854 "xxxx 2 17 v c c False\n",
855 "xxxx 2 18 v g u False\n",
856 "xxxx 2 19 v e v False\n",
857 "xxxx 2 20 v b c False\n",
858 "seq1 3 0 u ! v False\n",
859 "xxxx 3 1 u c a False\n",
860 "xxxx 3 2 u a f False\n",
861 "seq1 3 3 u f u True\n",
862 "xxxx 3 4 u e z False\n",
863 "xxxx 3 5 u h y False\n",
864 "xxxx 3 6 u b w False\n",
865 "xxxx 3 7 u h e False\n",
866 "xxxx 3 8 u f u False\n",
867 "xxxx 3 9 u d h False\n",
868 "xxxx 3 10 u c x False\n",
869 "xxxx 3 11 u c b False\n",
870 "xxxx 3 12 u f h False\n",
871 "xxxx 3 13 u a z False\n",
872 "xxxx 3 14 u e f False\n",
873 "xxxx 3 15 u e d False\n",
874 "xxxx 3 16 u b c False\n",
875 "xxxx 3 17 u c u False\n",
876 "xxxx 3 18 u g v False\n",
877 "xxxx 3 19 u e c False\n",
878 "xxxx 3 20 u b f False\n",
879 "seq1 4 0 z ! a False\n",
880 "xxxx 4 1 z c f False\n",
881 "xxxx 4 2 z a u False\n",
882 "seq1 4 3 z f z True\n",
883 "xxxx 4 4 z e y False\n",
884 "xxxx 4 5 z h w False\n",
885 "xxxx 4 6 z b e False\n",
886 "xxxx 4 7 z h u False\n",
887 "xxxx 4 8 z f h False\n",
888 "xxxx 4 9 z d x False\n",
889 "xxxx 4 10 z c b False\n",
890 "xxxx 4 11 z c h False\n",
891 "xxxx 4 12 z f z False\n",
892 "xxxx 4 13 z a f False\n",
893 "xxxx 4 14 z e d False\n",
894 "xxxx 4 15 z e c False\n",
895 "xxxx 4 16 z b u False\n",
896 "xxxx 4 17 z c v False\n",
897 "xxxx 4 18 z g c False\n",
898 "xxxx 4 19 z e f False\n",
899 "xxxx 4 20 z b a False\n",
900 "seq1 5 0 y ! f False\n",
901 "xxxx 5 1 y c u False\n",
902 "xxxx 5 2 y a z False\n",
903 "seq1 5 3 y f y True\n",
904 "xxxx 5 4 y e w False\n",
905 "xxxx 5 5 y h e False\n",
906 "xxxx 5 6 y b u False\n",
907 "xxxx 5 7 y h h False\n",
908 "xxxx 5 8 y f x False\n",
909 "xxxx 5 9 y d b False\n",
910 "xxxx 5 10 y c h False\n",
911 "xxxx 5 11 y c z False\n",
912 "xxxx 5 12 y f f False\n",
913 "xxxx 5 13 y a d False\n",
914 "xxxx 5 14 y e c False\n",
915 "xxxx 5 15 y e u False\n",
916 "xxxx 5 16 y b v False\n",
917 "xxxx 5 17 y c c False\n",
918 "xxxx 5 18 y g f False\n",
919 "xxxx 5 19 y e a False\n",
920 "xxxx 5 20 y b y False\n",
921 "seq1 6 0 w ! u False\n",
922 "xxxx 6 1 w c z False\n",
923 "xxxx 6 2 w a y False\n",
924 "seq1 6 3 w f w True\n",
925 "seq2 6 4 w e e True\n",
926 "xxxx 6 5 w h u False\n",
927 "xxxx 6 6 w b h False\n",
928 "xxxx 6 7 w h x False\n",
929 "xxxx 6 8 w f b False\n",
930 "xxxx 6 9 w d h False\n",
931 "xxxx 6 10 w c z False\n",
932 "xxxx 6 11 w c f False\n",
933 "xxxx 6 12 w f d False\n",
934 "xxxx 6 13 w a c False\n",
935 "xxxx 6 14 w e u False\n",
936 "xxxx 6 15 w e v False\n",
937 "xxxx 6 16 w b c False\n",
938 "xxxx 6 17 w c f False\n",
939 "xxxx 6 18 w g a False\n",
940 "xxxx 6 19 w e y False\n",
941 "xxxx 6 20 w b y False\n",
942 "seq1 7 0 u ! z False\n",
943 "xxxx 7 1 u c y False\n",
944 "xxxx 7 2 u a w False\n",
945 "xxxx 7 3 u f e False\n",
946 "seq1 7 4 u e u True\n",
947 "seq2 7 5 u h h True\n",
948 "xxxx 7 6 u b x False\n",
949 "xxxx 7 7 u h b False\n",
950 "xxxx 7 8 u f h False\n",
951 "xxxx 7 9 u d z False\n",
952 "xxxx 7 10 u c f False\n",
953 "xxxx 7 11 u c d False\n",
954 "xxxx 7 12 u f c False\n",
955 "xxxx 7 13 u a u False\n",
956 "xxxx 7 14 u e v False\n",
957 "xxxx 7 15 u e c False\n",
958 "xxxx 7 16 u b f False\n",
959 "xxxx 7 17 u c a False\n",
960 "xxxx 7 18 u g y False\n",
961 "xxxx 7 19 u e y False\n",
962 "xxxx 7 20 u b y False\n",
963 "seq1 8 0 x ! y False\n",
964 "xxxx 8 1 x c w False\n",
965 "xxxx 8 2 x a e False\n",
966 "xxxx 8 3 x f u False\n",
967 "xxxx 8 4 x e h False\n",
968 "seq1 8 5 x h x True\n",
969 "seq2 8 6 x b b True\n",
970 "seq2 8 7 x h h True\n",
971 "xxxx 8 8 x f z False\n",
972 "xxxx 8 9 x d f False\n",
973 "xxxx 8 10 x c d False\n",
974 "xxxx 8 11 x c c False\n",
975 "xxxx 8 12 x f u False\n",
976 "xxxx 8 13 x a v False\n",
977 "xxxx 8 14 x e c False\n",
978 "xxxx 8 15 x e f False\n",
979 "xxxx 8 16 x b a False\n",
980 "xxxx 8 17 x c y False\n",
981 "xxxx 8 18 x g y False\n",
982 "xxxx 8 19 x e y False\n",
983 "xxxx 8 20 x b u False\n",
984 "seq1 9 0 z ! w False\n",
985 "xxxx 9 1 z c e False\n",
986 "xxxx 9 2 z a u False\n",
987 "xxxx 9 3 z f h False\n",
988 "xxxx 9 4 z e x False\n",
989 "xxxx 9 5 z h b False\n",
990 "xxxx 9 6 z b h False\n",
991 "seq1 9 7 z h z True\n",
992 "seq2 9 8 z f f True\n",
993 "seq2 9 9 z d d True\n",
994 "seq2 9 10 z c c True\n",
995 "xxxx 9 11 z c u False\n",
996 "xxxx 9 12 z f v False\n",
997 "xxxx 9 13 z a c False\n",
998 "xxxx 9 14 z e f False\n",
999 "xxxx 9 15 z e a False\n",
1000 "xxxx 9 16 z b y False\n",
1001 "xxxx 9 17 z c y False\n",
1002 "xxxx 9 18 z g y False\n",
1003 "xxxx 9 19 z e u False\n",
1004 "xxxx 9 20 z b e False\n",
1005 "seq1 10 0 u ! e False\n",
1006 "xxxx 10 1 u c u False\n",
1007 "xxxx 10 2 u a h False\n",
1008 "xxxx 10 3 u f x False\n",
1009 "xxxx 10 4 u e b False\n",
1010 "xxxx 10 5 u h h False\n",
1011 "xxxx 10 6 u b z False\n",
1012 "xxxx 10 7 u h f False\n",
1013 "xxxx 10 8 u f d False\n",
1014 "xxxx 10 9 u d c False\n",
1015 "seq1 10 10 u c u True\n",
1016 "xxxx 10 11 u c v False\n",
1017 "xxxx 10 12 u f c False\n",
1018 "xxxx 10 13 u a f False\n",
1019 "xxxx 10 14 u e a False\n",
1020 "xxxx 10 15 u e y False\n",
1021 "xxxx 10 16 u b y False\n",
1022 "xxxx 10 17 u c y False\n",
1023 "xxxx 10 18 u g u False\n",
1024 "xxxx 10 19 u e e False\n",
1025 "xxxx 10 20 u b z False\n",
1026 "seq1 11 0 v ! u False\n",
1027 "xxxx 11 1 v c h False\n",
1028 "xxxx 11 2 v a x False\n",
1029 "xxxx 11 3 v f b False\n",
1030 "xxxx 11 4 v e h False\n",
1031 "xxxx 11 5 v h z False\n",
1032 "xxxx 11 6 v b f False\n",
1033 "xxxx 11 7 v h d False\n",
1034 "xxxx 11 8 v f c False\n",
1035 "xxxx 11 9 v d u False\n",
1036 "seq1 11 10 v c v True\n",
1037 "seq2 11 11 v c c True\n",
1038 "seq2 11 12 v f f True\n",
1039 "seq2 11 13 v a a True\n",
1040 "xxxx 11 14 v e y False\n",
1041 "xxxx 11 15 v e y False\n",
1042 "xxxx 11 16 v b y False\n",
1043 "xxxx 11 17 v c u False\n",
1044 "xxxx 11 18 v g e False\n",
1045 "xxxx 11 19 v e z False\n",
1046 "xxxx 11 20 v b e False\n",
1047 "seq1 12 0 y ! h False\n",
1048 "xxxx 12 1 y c x False\n",
1049 "xxxx 12 2 y a b False\n",
1050 "xxxx 12 3 y f h False\n",
1051 "xxxx 12 4 y e z False\n",
1052 "xxxx 12 5 y h f False\n",
1053 "xxxx 12 6 y b d False\n",
1054 "xxxx 12 7 y h c False\n",
1055 "xxxx 12 8 y f u False\n",
1056 "xxxx 12 9 y d v False\n",
1057 "xxxx 12 10 y c c False\n",
1058 "xxxx 12 11 y c f False\n",
1059 "xxxx 12 12 y f a False\n",
1060 "seq1 12 13 y a y True\n",
1061 "xxxx 12 14 y e y False\n",
1062 "xxxx 12 15 y e y False\n",
1063 "xxxx 12 16 y b u False\n",
1064 "xxxx 12 17 y c e False\n",
1065 "xxxx 12 18 y g z False\n",
1066 "xxxx 12 19 y e e False\n",
1067 "xxxx 12 20 y b b False\n",
1068 "seq1 13 0 y ! x False\n",
1069 "xxxx 13 1 y c b False\n",
1070 "xxxx 13 2 y a h False\n",
1071 "xxxx 13 3 y f z False\n",
1072 "xxxx 13 4 y e f False\n",
1073 "xxxx 13 5 y h d False\n",
1074 "xxxx 13 6 y b c False\n",
1075 "xxxx 13 7 y h u False\n",
1076 "xxxx 13 8 y f v False\n",
1077 "xxxx 13 9 y d c False\n",
1078 "xxxx 13 10 y c f False\n",
1079 "xxxx 13 11 y c a False\n",
1080 "xxxx 13 12 y f y False\n",
1081 "seq1 13 13 y a y True\n",
1082 "xxxx 13 14 y e y False\n",
1083 "xxxx 13 15 y e u False\n",
1084 "xxxx 13 16 y b e False\n",
1085 "xxxx 13 17 y c z False\n",
1086 "xxxx 13 18 y g e False\n",
1087 "xxxx 13 19 y e b False\n",
1088 "xxxx 13 20 y b c False\n",
1089 "seq1 14 0 y ! b False\n",
1090 "xxxx 14 1 y c h False\n",
1091 "xxxx 14 2 y a z False\n",
1092 "xxxx 14 3 y f f False\n",
1093 "xxxx 14 4 y e d False\n",
1094 "xxxx 14 5 y h c False\n",
1095 "xxxx 14 6 y b u False\n",
1096 "xxxx 14 7 y h v False\n",
1097 "xxxx 14 8 y f c False\n",
1098 "xxxx 14 9 y d f False\n",
1099 "xxxx 14 10 y c a False\n",
1100 "xxxx 14 11 y c y False\n",
1101 "xxxx 14 12 y f y False\n",
1102 "seq1 14 13 y a y True\n",
1103 "xxxx 14 14 y e u False\n",
1104 "xxxx 14 15 y e e False\n",
1105 "xxxx 14 16 y b z False\n",
1106 "xxxx 14 17 y c e False\n",
1107 "xxxx 14 18 y g b False\n",
1108 "xxxx 14 19 y e c False\n",
1109 "xxxx 14 20 y b g False\n",
1110 "seq1 15 0 u ! h False\n",
1111 "xxxx 15 1 u c z False\n",
1112 "xxxx 15 2 u a f False\n",
1113 "xxxx 15 3 u f d False\n",
1114 "xxxx 15 4 u e c False\n",
1115 "xxxx 15 5 u h u False\n",
1116 "xxxx 15 6 u b v False\n",
1117 "xxxx 15 7 u h c False\n",
1118 "xxxx 15 8 u f f False\n",
1119 "xxxx 15 9 u d a False\n",
1120 "xxxx 15 10 u c y False\n",
1121 "xxxx 15 11 u c y False\n",
1122 "xxxx 15 12 u f y False\n",
1123 "seq1 15 13 u a u True\n",
1124 "seq2 15 14 u e e True\n",
1125 "xxxx 15 15 u e z False\n",
1126 "xxxx 15 16 u b e False\n",
1127 "xxxx 15 17 u c b False\n",
1128 "xxxx 15 18 u g c False\n",
1129 "xxxx 15 19 u e g False\n",
1130 "xxxx 15 20 u b w False\n",
1131 "seq1 16 0 z ! z False\n",
1132 "xxxx 16 1 z c f False\n",
1133 "xxxx 16 2 z a d False\n",
1134 "xxxx 16 3 z f c False\n",
1135 "xxxx 16 4 z e u False\n",
1136 "xxxx 16 5 z h v False\n",
1137 "xxxx 16 6 z b c False\n",
1138 "xxxx 16 7 z h f False\n",
1139 "xxxx 16 8 z f a False\n",
1140 "xxxx 16 9 z d y False\n",
1141 "xxxx 16 10 z c y False\n",
1142 "xxxx 16 11 z c y False\n",
1143 "xxxx 16 12 z f u False\n",
1144 "xxxx 16 13 z a e False\n",
1145 "seq1 16 14 z e z True\n",
1146 "seq2 16 15 z e e True\n",
1147 "seq2 16 16 z b b True\n",
1148 "seq2 16 17 z c c True\n",
1149 "seq2 16 18 z g g True\n",
1150 "xxxx 16 19 z e w False\n",
1151 "xxxx 16 20 z b u False\n",
1152 "seq1 17 0 w ! f False\n",
1153 "xxxx 17 1 w c d False\n",
1154 "xxxx 17 2 w a c False\n",
1155 "xxxx 17 3 w f u False\n",
1156 "xxxx 17 4 w e v False\n",
1157 "xxxx 17 5 w h c False\n",
1158 "xxxx 17 6 w b f False\n",
1159 "xxxx 17 7 w h a False\n",
1160 "xxxx 17 8 w f y False\n",
1161 "xxxx 17 9 w d y False\n",
1162 "xxxx 17 10 w c y False\n",
1163 "xxxx 17 11 w c u False\n",
1164 "xxxx 17 12 w f e False\n",
1165 "xxxx 17 13 w a z False\n",
1166 "xxxx 17 14 w e e False\n",
1167 "xxxx 17 15 w e b False\n",
1168 "xxxx 17 16 w b c False\n",
1169 "xxxx 17 17 w c g False\n",
1170 "seq1 17 18 w g w True\n",
1171 "xxxx 17 19 w e u False\n",
1172 "xxxx 17 20 w b e False\n",
1173 "seq1 18 0 u ! d False\n",
1174 "xxxx 18 1 u c c False\n",
1175 "xxxx 18 2 u a u False\n",
1176 "xxxx 18 3 u f v False\n",
1177 "xxxx 18 4 u e c False\n",
1178 "xxxx 18 5 u h f False\n",
1179 "xxxx 18 6 u b a False\n",
1180 "xxxx 18 7 u h y False\n",
1181 "xxxx 18 8 u f y False\n",
1182 "xxxx 18 9 u d y False\n",
1183 "xxxx 18 10 u c u False\n",
1184 "xxxx 18 11 u c e False\n",
1185 "xxxx 18 12 u f z False\n",
1186 "xxxx 18 13 u a e False\n",
1187 "xxxx 18 14 u e b False\n",
1188 "xxxx 18 15 u e c False\n",
1189 "xxxx 18 16 u b g False\n",
1190 "xxxx 18 17 u c w False\n",
1191 "seq1 18 18 u g u True\n",
1192 "seq2 18 19 u e e True\n",
1193 "xxxx 18 20 u b w False\n",
1194 "seq1 19 0 w ! c False\n",
1195 "xxxx 19 1 w c u False\n",
1196 "xxxx 19 2 w a v False\n",
1197 "xxxx 19 3 w f c False\n",
1198 "xxxx 19 4 w e f False\n",
1199 "xxxx 19 5 w h a False\n",
1200 "xxxx 19 6 w b y False\n",
1201 "xxxx 19 7 w h y False\n",
1202 "xxxx 19 8 w f y False\n",
1203 "xxxx 19 9 w d u False\n",
1204 "xxxx 19 10 w c e False\n",
1205 "xxxx 19 11 w c z False\n",
1206 "xxxx 19 12 w f e False\n",
1207 "xxxx 19 13 w a b False\n",
1208 "xxxx 19 14 w e c False\n",
1209 "xxxx 19 15 w e g False\n",
1210 "xxxx 19 16 w b w False\n",
1211 "xxxx 19 17 w c u False\n",
1212 "xxxx 19 18 w g e False\n",
1213 "seq1 19 19 w e w True\n",
1214 "seq2 19 20 w b b True\n",
1215 "seq1 20 0 y ! u False\n",
1216 "xxxx 20 1 y c v False\n",
1217 "xxxx 20 2 y a c False\n",
1218 "xxxx 20 3 y f f False\n",
1219 "xxxx 20 4 y e a False\n",
1220 "xxxx 20 5 y h y False\n",
1221 "xxxx 20 6 y b y False\n",
1222 "xxxx 20 7 y h y False\n",
1223 "xxxx 20 8 y f u False\n",
1224 "xxxx 20 9 y d e False\n",
1225 "xxxx 20 10 y c z False\n",
1226 "xxxx 20 11 y c e False\n",
1227 "xxxx 20 12 y f b False\n",
1228 "xxxx 20 13 y a c False\n",
1229 "xxxx 20 14 y e g False\n",
1230 "xxxx 20 15 y e w False\n",
1231 "xxxx 20 16 y b u False\n",
1232 "xxxx 20 17 y c e False\n",
1233 "xxxx 20 18 y g w False\n",
1234 "xxxx 20 19 y e b False\n",
1235 "seq1 20 20 y b y True\n",
1236 "T . . . . . . . . . . . . . . . . . . . .\n",
1237 "T T . . . . . . . . . . . . . . . . . . .\n",
1238 ". T T T . . . . . . . . . . . . . . . . .\n",
1239 ". . . T . . . . . . . . . . . . . . . . .\n",
1240 ". . . T . . . . . . . . . . . . . . . . .\n",
1241 ". . . T . . . . . . . . . . . . . . . . .\n",
1242 ". . . T T . . . . . . . . . . . . . . . .\n",
1243 ". . . . T T . . . . . . . . . . . . . . .\n",
1244 ". . . . . T T T . . . . . . . . . . . . .\n",
1245 ". . . . . . . T T T T . . . . . . . . . .\n",
1246 ". . . . . . . . . . T . . . . . . . . . .\n",
1247 ". . . . . . . . . . T T T T . . . . . . .\n",
1248 ". . . . . . . . . . . . . T . . . . . . .\n",
1249 ". . . . . . . . . . . . . T . . . . . . .\n",
1250 ". . . . . . . . . . . . . T . . . . . . .\n",
1251 ". . . . . . . . . . . . . T T . . . . . .\n",
1252 ". . . . . . . . . . . . . . T T T T T . .\n",
1253 ". . . . . . . . . . . . . . . . . . T . .\n",
1254 ". . . . . . . . . . . . . . . . . . T T .\n",
1255 ". . . . . . . . . . . . . . . . . . . T T\n",
1256 ". . . . . . . . . . . . . . . . . . . . T\n"
1261 "v, bp, t = is_interleave(s2, s1, il, return_backpointers=True, return_table=True, debug=True)\n",
1262 "print(show_table(t))"
1266 "cell_type": "code",
1267 "execution_count": 22,
1273 "'XcVafUZYWeUhXbhZfdcUVcfaYYYUeZebcgWUeWbY'"
1276 "execution_count": 22,
1278 "output_type": "execute_result"
1282 "show_backtrace(bp)"
1286 "cell_type": "code",
1287 "execution_count": 23,
1292 "output_type": "stream",
1294 "T . . . . . . . . . . . . . . . . . . . .\n",
1295 "T T . . . . . . . . . . . . . . . . . . .\n",
1296 ". T T T . . . . . . . . . . . . . . . . .\n",
1297 ". . . T . . . . . . . . . . . . . . . . .\n",
1298 ". . . T . . . . . . . . . . . . . . . . .\n",
1299 ". . . T . . . . . . . . . . . . . . . . .\n",
1300 ". . . T T . . . . . . . . . . . . . . . .\n",
1301 ". . . . T T . . . . . . . . . . . . . . .\n",
1302 ". . . . . T T T . . . . . . . . . . . . .\n",
1303 ". . . . . . . T T T T . . . . . . . . . .\n",
1304 ". . . . . . . . . . T . . . . . . . . . .\n",
1305 ". . . . . . . . . . T T T T . . . . . . .\n",
1306 ". . . . . . . . . . . . . T . . . . . . .\n",
1307 ". . . . . . . . . . . . . T . . . . . . .\n",
1308 ". . . . . . . . . . . . . T . . . . . . .\n",
1309 ". . . . . . . . . . . . . T T . . . . . .\n",
1310 ". . . . . . . . . . . . . . T T T T T . .\n",
1311 ". . . . . . . . . . . . . . . . . . T . .\n",
1312 ". . . . . . . . . . . . . . . . . . T T .\n",
1313 ". . . . . . . . . . . . . . . . . . . T T\n",
1314 ". . . . . . . . . . . . . . . . . . . . T\n",
1315 "XcVafUZYWeUhXbhZfdcUVcfaYYYUeZebcgWUeWbY\n"
1324 "execution_count": 23,
1326 "output_type": "execute_result"
1330 "v, bp, t = is_interleave(s2, s1, il, return_backpointers=True, return_table=True)\n",
1331 "print(show_table(t))\n",
1332 "print(show_backtrace(bp))\n",
1337 "cell_type": "code",
1338 "execution_count": 24,
1344 "('fdghaegbegehggbggcgcfecbgfacefhahahdhfafacchafacea',\n",
1345 " 'hdhadgebfeaehhhggbdghgcehabccgbddafeacagbgcahhfefe',\n",
1346 " 'fhdgdhahadgegebfbeegehaegghbhghggcggcfecbgbdgfhagcehabcccgbedfdhahaafeahcdhfaafaccghafbgacceahahfefe',\n",
1350 "execution_count": 24,
1352 "output_type": "execute_result"
1356 "s1 = make_string(50)\n",
1357 "s2 = make_string(50)\n",
1358 "il = interleave(s1, s2)\n",
1359 "s1, s2, il, len(il)"
1363 "cell_type": "code",
1364 "execution_count": 25,
1369 "output_type": "stream",
1371 "T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1372 ". T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1373 ". T . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1374 ". . . T . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1375 ". . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1376 ". . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1377 ". . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1378 ". . . . . T . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1379 ". . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1380 ". . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1381 ". . . . . . . . T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1382 ". . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1383 ". . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1384 ". . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1385 ". . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1386 ". . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1387 ". . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1388 ". . . . . . . . . . . . . . . . T . T T T T T T T T . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1389 ". . . . . . . . . . . . . . . . . . . . . . . T . T . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1390 ". . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1391 ". . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . .\n",
1392 ". . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . .\n",
1393 ". . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . .\n",
1394 ". . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . .\n",
1395 ". . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . .\n",
1396 ". . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . .\n",
1397 ". . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . .\n",
1398 ". . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . .\n",
1399 ". . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . .\n",
1400 ". . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . .\n",
1401 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . .\n",
1402 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . .\n",
1403 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . .\n",
1404 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T . . . . . . . . . . . . . . . .\n",
1405 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . T T . . . . . . . . . . . . . . . .\n",
1406 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . .\n",
1407 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . .\n",
1408 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . .\n",
1409 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T . . . . . . . . . . .\n",
1410 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T T . . . . . . .\n",
1411 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . .\n",
1412 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . .\n",
1413 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . .\n",
1414 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T\n",
1415 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T .\n",
1416 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T\n",
1417 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1418 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1419 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1420 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1421 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1422 "fHdgDhaHADGegEBFbeEgehAEggHbHgHgGcgGcfecbgBDGfHaGCEHABcCCGBeDfDhahaAFEAhCdhfaAfaccGhafBGacCeAHaHFEFE\n"
1431 "execution_count": 25,
1433 "output_type": "execute_result"
1437 "v, bp, t = is_interleave(s2, s1, il, return_backpointers=True, return_table=True)\n",
1438 "print(show_table(t))\n",
1439 "print(show_backtrace(bp))\n",
1444 "cell_type": "code",
1445 "execution_count": 26,
1450 "output_type": "stream",
1452 "1000 loops, best of 3: 1.4 ms per loop\n"
1458 "is_interleave(s2, s1, il)"
1462 "cell_type": "code",
1463 "execution_count": 27,
1468 "output_type": "stream",
1470 "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1471 "T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1472 ". T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1473 ". T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1474 ". . T . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1475 ". . T T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1476 ". . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1477 ". . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1478 ". . . . . . . T . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1479 ". . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1480 ". . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1481 ". . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1482 ". . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1483 ". . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1484 ". . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1485 ". . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1486 ". . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1487 ". . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1488 ". . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1489 ". . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1490 ". . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1491 ". . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1492 ". . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1493 ". . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1494 ". . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1495 ". . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1496 ". . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1497 ". . . . . . . . . . . . . . . . . . . . . T T T T T T T T T . . . . . . . . . . . . . . . . . . . . .\n",
1498 ". . . . . . . . . . . . . . . . . . . . . . T . . . . T T T T T . . . . . . . . . . . . . . . . . . .\n",
1499 ". . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . T T . . . . . . . . . . . . . . . . . .\n",
1500 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . .\n",
1501 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . .\n",
1502 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . .\n",
1503 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . .\n",
1504 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T . . . . . . . . . . . . .\n",
1505 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . .\n",
1506 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . .\n",
1507 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . .\n",
1508 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . .\n",
1509 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . .\n",
1510 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . .\n",
1511 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . .\n",
1512 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . .\n",
1513 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . .\n",
1514 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . .\n",
1515 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . .\n",
1516 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . .\n",
1517 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . .\n",
1518 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . .\n",
1519 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . .\n",
1520 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . T T T T T T\n",
1521 "FhDGdhaHAdgEGebfBeEGEHaeGGhBhGhgGCgGCFECBGbdgFhAgcehabccCgbEdFdHAHaAfeaHcDHFaAFACCgHAFbgAcCEahAhfefe\n"
1530 "execution_count": 27,
1532 "output_type": "execute_result"
1536 "v, bp, t = is_interleave(s1, s2, il, return_backpointers=True, return_table=True)\n",
1537 "print(show_table(t))\n",
1538 "print(show_backtrace(bp))\n",
1543 "cell_type": "code",
1544 "execution_count": 28,
1553 "execution_count": 28,
1555 "output_type": "execute_result"
1559 "show_backtrace(bp).lower() == il"
1563 "cell_type": "code",
1564 "execution_count": 29,
1570 "('febffabcddaaaeffcdhcdaffgfafafcchfffdcbbbagbdfdbdd', False, False)"
1573 "execution_count": 29,
1575 "output_type": "execute_result"
1579 "s3 = make_string(50)\n",
1580 "s3, is_interleave(s1, s3, il), is_interleave(s2, s3, il)"
1584 "cell_type": "code",
1585 "execution_count": 30,
1590 "output_type": "stream",
1592 "T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1593 "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1594 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1595 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1596 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1597 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1598 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1599 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1600 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1601 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1602 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1603 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1604 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1605 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1606 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1607 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1608 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1609 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1610 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1611 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1612 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1613 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1614 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1615 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1616 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1617 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1618 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1619 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1620 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1621 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1622 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1623 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1624 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1625 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1626 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1627 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1628 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1629 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1630 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1631 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1632 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1633 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1634 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1635 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1636 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1637 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1638 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1639 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1640 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1641 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1642 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1652 "execution_count": 30,
1654 "output_type": "execute_result"
1658 "v, bp, t = is_interleave(s1, s3, il, return_backpointers=True, return_table=True)\n",
1659 "print(show_table(t))\n",
1660 "print(show_backtrace(bp))\n",
1665 "cell_type": "code",
1666 "execution_count": 31,
1672 "def is_interleave_recursive(s1, s2, s3):\n",
1674 " return s2 == s3\n",
1676 " return s1 == s3\n",
1678 " if s1[-1] == s2[-1] and s1[-1] == s3[-1]:\n",
1679 " return is_interleave_recursive(s1[:-1], s2, s3[:-1]) or is_interleave(s1, s2[:-1], s3[:-1])\n",
1680 " elif s1[-1] == s3[-1]:\n",
1681 " return is_interleave_recursive(s1[:-1], s2, s3[:-1])\n",
1682 " elif s2[-1] == s3[-1]:\n",
1683 " return is_interleave(s1, s2[:-1], s3[:-1])\n",
1689 "cell_type": "code",
1690 "execution_count": 32,
1696 "s1 = make_string(500)\n",
1697 "s2 = make_string(500)\n",
1698 "s3 = make_string(500)\n",
1699 "s12 = interleave(s1, s2)\n",
1700 "s23 = interleave(s2, s3)"
1704 "cell_type": "code",
1705 "execution_count": 33,
1714 "execution_count": 33,
1716 "output_type": "execute_result"
1720 "is_interleave_recursive(s1, s2, s12)"
1724 "cell_type": "code",
1725 "execution_count": 34,
1734 "execution_count": 34,
1736 "output_type": "execute_result"
1740 "is_interleave_recursive(s1, s2, s23)"
1744 "cell_type": "markdown",
1751 "cell_type": "code",
1752 "execution_count": 35,
1758 "def show_annotated_table(table, bps):\n",
1759 " return '\\n'.join(' '.join('*' if (i, j) == (0, 0) else bps[i, j][2] if table[i, j] else '.' for j in sorted(set([k[1] for k in table])))\n",
1760 " for i in sorted(set([k[0] for k in table])))"
1764 "cell_type": "code",
1765 "execution_count": 36,
1771 "def show_backtrace_star(bps):\n",
1772 " i = max([0] + [k[0] for k in bps])\n",
1773 " j = max([0] + [k[1] for k in bps])\n",
1776 " if (i, j) in bps:\n",
1777 " while i != 0 or j != 0:\n",
1778 " chars += bps[i, j][2]\n",
1779 " if bps[i, j][3] == 'seq1':\n",
1783 " i, j = bps[i, j][0], bps[i, j][1] \n",
1784 " return ''.join(list(reversed(chars))) + '\\n' + ''.join(list(reversed(stars)))\n",
1790 "cell_type": "code",
1791 "execution_count": 37,
1796 "output_type": "stream",
1800 "2: bdccbaadcbdbdacacaac\n",
1802 "4: dcccaadcdddcdbbbadbc\n",
1803 "5: bcdbddaccbddbbdaabca\n",
1804 "6: cdcccadbaadcddcbcaac\n"
1810 "['bcdbddaccbddbbdaabca']"
1813 "execution_count": 37,
1815 "output_type": "execute_result"
1819 "s1 = make_string(10, alphabet='abcd')\n",
1820 "s2 = make_string(10, alphabet='abcd')\n",
1821 "s3 = make_string(10, alphabet='abcd')\n",
1822 "s4 = make_string(10, alphabet='abcd')\n",
1823 "il = interleave(s1, s2)\n",
1824 "bs = [s3, il, interleave(s3, s4), interleave(s2, s4), interleave(s1, s3)]\n",
1825 "random.shuffle(bs)\n",
1826 "bs = [s1, s2] + bs\n",
1827 "tg = [l for l in bs if is_interleave(s1, s2, l)]\n",
1828 "print('\\n'.join(['{}: {}'.format(i, s) for i, s in enumerate(bs)]))\n",
1833 "cell_type": "code",
1834 "execution_count": 38,
1839 "output_type": "stream",
1841 "* b . . . . . . . . .\n",
1842 ". c d b . . . . . . .\n",
1843 ". d . d . . . . . . .\n",
1844 ". . . d a c . . . . .\n",
1845 ". . . . c c b d . . .\n",
1846 ". . . . . . d d . . .\n",
1847 ". . . . . . . b . . .\n",
1848 ". . . . . . . b . . .\n",
1849 ". . . . . . . d a a .\n",
1850 ". . . . . . . . . b .\n",
1851 ". . . . . . . . . c a\n",
1852 "bCdbDDacCbdDBBDaaBCa\n",
1853 "bcdbddaccbddbbdaabca\n",
1854 " * ** * **** ** \n"
1863 "execution_count": 38,
1865 "output_type": "execute_result"
1869 "v, bp, t = is_interleave(s1, s2, il, return_backpointers=True, return_table=True)\n",
1870 "print(show_annotated_table(t, bp))\n",
1871 "print(show_backtrace(bp))\n",
1872 "print(show_backtrace_star(bp))\n",
1877 "cell_type": "code",
1878 "execution_count": 39,
1883 "output_type": "stream",
1885 "dcccaadcdddcdbbbadbc\n",
1895 "execution_count": 39,
1897 "output_type": "execute_result"
1901 "ind = [i for i, b in enumerate(bs) if is_interleave(s1, s3, b)][0]\n",
1902 "v, bp = is_interleave(s1, s3, bs[ind], return_backpointers=True)\n",
1903 "print(show_backtrace_star(bp))\n",
1908 "cell_type": "code",
1909 "execution_count": 40,
1914 "output_type": "stream",
1916 "* . . . . . . . . . .\n",
1917 "b c d . . . . . . . .\n",
1918 ". d . . . . . . . . .\n",
1919 ". b d d . . . . . . .\n",
1920 ". . . a c . . . . . .\n",
1921 ". . . c c . . . . . .\n",
1922 ". . . . b d . . . . .\n",
1923 ". . . . d d b b d . .\n",
1924 ". . . . . . . . a . .\n",
1925 ". . . . . . . . a b c\n",
1926 ". . . . . . . . . . a\n",
1927 "BcDBddAcCBdDbbdAAbcA\n",
1928 "bcdbddaccbddbbdaabca\n",
1929 "* ** * ** * ** *\n"
1938 "execution_count": 40,
1940 "output_type": "execute_result"
1944 "v, bp, t = is_interleave(s2, s1, il, return_backpointers=True, return_table=True)\n",
1945 "print(show_annotated_table(t, bp))\n",
1946 "print(show_backtrace(bp))\n",
1947 "print(show_backtrace_star(bp))\n",
1952 "cell_type": "code",
1953 "execution_count": 41,
1958 "output_type": "stream",
1960 "* . . . . . . . . . .\n",
1961 ". . . . . . . . . . .\n",
1962 ". . . . . . . . . . .\n",
1963 ". . . . . . . . . . .\n",
1964 ". . . . . . . . . . .\n",
1965 ". . . . . . . . . . .\n",
1966 ". . . . . . . . . . .\n",
1967 ". . . . . . . . . . .\n",
1968 ". . . . . . . . . . .\n",
1969 ". . . . . . . . . . .\n",
1970 ". . . . . . . . . . .\n",
1981 "execution_count": 41,
1983 "output_type": "execute_result"
1987 "v, bp, t = is_interleave(s1, s3, il, return_backpointers=True, return_table=True)\n",
1988 "print(show_annotated_table(t, bp))\n",
1989 "print(show_backtrace(bp))\n",
1990 "print(show_backtrace_star(bp))\n",
1995 "cell_type": "code",
1996 "execution_count": 42,
2001 "output_type": "stream",
2003 "* . . . . . . . . . .\n",
2004 "b . . . . . . . . . .\n",
2005 ". . . . . . . . . . .\n",
2006 ". . . . . . . . . . .\n",
2007 ". . . . . . . . . . .\n",
2008 ". . . . . . . . . . .\n",
2009 ". . . . . . . . . . .\n",
2010 ". . . . . . . . . . .\n",
2011 ". . . . . . . . . . .\n",
2012 ". . . . . . . . . . .\n",
2013 ". . . . . . . . . . .\n",
2025 "execution_count": 42,
2027 "output_type": "execute_result"
2031 "v, bp, t = is_interleave(s2, s3, il, return_backpointers=True, return_table=True)\n",
2032 "print(show_annotated_table(t, bp))\n",
2033 "print(show_backtrace(bp))\n",
2034 "print(show_backtrace_star(bp))\n",
2039 "cell_type": "markdown",
2044 "# Make puzzle data\n",
2046 "## Note to self\n",
2047 "Include some distractors in the test set, such that:\n",
2048 "* subsequence(my_bill, distractor) is true\n",
2049 "* subsequence(friend_bill, distractor) is true\n",
2050 "* interleave(my_bill, friend_bill, distractor) is false\n",
2052 "(i.e. characters are shared between my_bill and friend_bill)\n",
2054 "Students are taking a greedy approach to subsequence, and saying the interleave is true if both bills are subsequences of the distractor.\n",
2056 "i.e. \"aaa\" and \"aab\" are both subsequences of \"aaabbb\", but cannot be interleaved to form \"aaabbb\".\n"
2060 "cell_type": "code",
2061 "execution_count": 43,
2067 "my_bill = make_string(200)\n",
2068 "friend_bill = make_string(200)\n",
2069 "other_bills = [make_string(200) for _ in range(98)]\n",
2071 "target_interleaved = interleave(my_bill, friend_bill)\n",
2072 "mine_interleaved = [interleave(my_bill, o) for o in random.sample(other_bills, 21)]\n",
2073 "friend_interleaved = [interleave(friend_bill, o) for o in random.sample(other_bills, 13)]\n",
2074 "other_interleaved = []\n",
2075 "for _ in range(103):\n",
2076 " s1, s2 = random.sample(other_bills, 2)\n",
2077 " other_interleaved += [interleave(s1, s2)]"
2081 "cell_type": "code",
2082 "execution_count": 44,
2088 "all_targets = [target_interleaved] + mine_interleaved + friend_interleaved + other_interleaved"
2092 "cell_type": "code",
2093 "execution_count": 45,
2098 "output_type": "stream",
2100 "CPU times: user 3.4 s, sys: 0 ns, total: 3.4 s\n",
2101 "Wall time: 3.4 s\n"
2110 "execution_count": 45,
2112 "output_type": "execute_result"
2116 "%time [i for i, s12 in enumerate(all_targets) if is_interleave(my_bill, friend_bill, s12)]"
2120 "cell_type": "code",
2121 "execution_count": 46,
2126 "output_type": "stream",
2128 "CPU times: user 932 ms, sys: 0 ns, total: 932 ms\n",
2129 "Wall time: 932 ms\n"
2138 "execution_count": 46,
2140 "output_type": "execute_result"
2144 "%time [i for i, s12 in enumerate(all_targets) if is_interleave_recursive(my_bill, friend_bill, s12)]"
2148 "cell_type": "code",
2149 "execution_count": 47,
2155 "bill_set = all_targets + random.sample(other_bills, 8)\n",
2156 "random.shuffle(bill_set)\n",
2157 "bill_set = [my_bill, friend_bill] + bill_set\n",
2159 "# with open('09-bills.txt', 'w') as f:\n",
2160 "# for i, b in enumerate(bill_set):\n",
2161 "# f.write('{}: {}\\n'.format(i, b))"
2165 "cell_type": "code",
2166 "execution_count": 51,
2172 "def is_subseq_greedy(s1, s2):\n",
2174 " while i < len(s1) and j < len(s2):\n",
2175 " if s1[i] == s2[j]:\n",
2178 " return i == len(s1)"
2182 "cell_type": "code",
2183 "execution_count": 94,
2189 "def subseq_partition(s1, s2):\n",
2191 " remainder = ''\n",
2192 " while i < len(s1) and j < len(s2):\n",
2193 " if s1[i] == s2[j]:\n",
2196 " remainder += s2[j]\n",
2198 " return i == len(s1), remainder"
2202 "cell_type": "code",
2203 "execution_count": 88,
2212 "execution_count": 88,
2214 "output_type": "execute_result"
2218 "common = make_string(10)\n",
2219 "padding = make_string(10)\n",
2220 "middle = interleave(common, padding)\n",
2222 "pre1 = make_string(5)\n",
2223 "suf1 = make_string(5)\n",
2225 "pre2 = make_string(5)\n",
2226 "suf2 = make_string(5)\n",
2228 "pre = interleave(pre1, pre2)\n",
2229 "suf = interleave(suf1, suf2)\n",
2231 "distractor = pre + middle + suf\n",
2233 "sub1 = pre1 + common + suf1\n",
2234 "sub2 = pre2 + common + suf2\n",
2236 "valid = interleave(sub1, sub2)\n",
2238 "len(distractor), len(valid), len(sub1), len(sub2)"
2242 "cell_type": "code",
2243 "execution_count": 89,
2252 "execution_count": 89,
2254 "output_type": "execute_result"
2258 "is_subseq_greedy(sub1, distractor), is_subseq_greedy(sub2, distractor)"
2262 "cell_type": "code",
2263 "execution_count": 90,
2272 "execution_count": 90,
2274 "output_type": "execute_result"
2278 "is_subseq_greedy(sub1, valid), is_subseq_greedy(sub2, valid)"
2282 "cell_type": "code",
2283 "execution_count": 91,
2292 "execution_count": 91,
2294 "output_type": "execute_result"
2298 "is_interleave(sub1, sub2, distractor), is_interleave(sub1, sub2, valid)"
2302 "cell_type": "code",
2303 "execution_count": 93,
2309 "('efcfdffcdbcehdffghch',\n",
2310 " 'hhdgeffcdbcehdfhfded',\n",
2311 " 'hhefdcgefdffdhgcdbcdbbeebhdefgfhgfdehdch',\n",
2312 " 'hhdegeffcffcdfdbcefchdfdbchehfddeffghdch')"
2315 "execution_count": 93,
2317 "output_type": "execute_result"
2321 "sub1, sub2, distractor, valid"
2325 "cell_type": "code",
2326 "execution_count": 96,
2335 "execution_count": 96,
2337 "output_type": "execute_result"
2341 "a, b = subseq_partition(sub1, distractor)\n",
2346 "cell_type": "code",
2347 "execution_count": 98,
2353 "('hhdgeffcdbcehfdhfded', 'hhdgeffcdbcehdfhfded')"
2356 "execution_count": 98,
2358 "output_type": "execute_result"
2362 "a, b = subseq_partition(sub1, valid)\n",
2367 "cell_type": "code",
2368 "execution_count": null,
2378 "display_name": "Python 3",
2379 "language": "python",
2383 "codemirror_mode": {
2387 "file_extension": ".py",
2388 "mimetype": "text/x-python",
2390 "nbconvert_exporter": "python",
2391 "pygments_lexer": "ipython3",